I have a question from one of my homework sets:

"Let $f(x)$ = cos(sin($3x$)). Find the smallest positive integer $k$ so that $f(x) = f(x + \pi k).$"

I know it's simple, but I'm somewhat confused. If someone could just point me in the right direction, it would be greatly appreciated.

Please don't give the answer, just a little help on how I could arrive to the answer.



Hint: \begin{align}f(x+\pi)&=\cos\bigl(\sin(3(x+\pi)\bigr)\\&=\cos\bigl(-\sin(3x)\bigr)\\&=\cos\bigl(\sin(3x)\bigr).\end{align}


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